PUBLISHED VERSION

PUBLISHED VERSION

http://hdl.handle.net/2440/108460

Nigar Hashimzade, Gareth D. Myles, Frank Page, Matthew D.Rablen

Social networks and occupational choice: the endogenous formation of attitudes and beliefs about tax compliance

Journal of Economic Psychology, 2014; 40:134-146

© 2012 Elsevier B.V. All rights reserved. Open Access funded by Economic and Social Research Council, under a Creative Commons license

Originally published at:

http://doi.org/10.1016/j.joep.2012.09.002

PERMISSIONS

http://creativecommons.org/licenses/by/3.0/

7 November 2017

Social networks and occupational choice: The endogenous formation of attitudes and beliefs about tax compliance

Nigar Hashimzade

^a

, Gareth D. Myles

^b,c,⇑

, Frank Page

^d

, Matthew D. Rablen

^e

aUniversity of Reading, Whiteknights P.O. Box 217, Reading, Berkshire RG66AH, United Kingdom

bUniversity of Exeter, Streatham Court, Exeter, Devon EX44PU, United Kingdom

cInstitute for Fiscal Studies, 7 Ridgmount St., London WC1E 7AE, United Kingdom

dIndiana University, 107 S. Indiana Ave., Bloomington, IN 47405, United States

eBrunel University, Kingston Lane, Uxbridge, Middlesex UB8 3PH, United Kingdom

a r t i c l e i n f o

Article history:

Received 3 January 2012

Received in revised form 7 June 2012 Accepted 4 September 2012 Available online 18 September 2012

JEL classification:

H26 D85 Keywords:

Tax evasion Attitudes Beliefs Endogeneity Social network Agent-based modelling Bomb-crater effect

a b s t r a c t

The paper analyses the emergence of group-specific attitudes and beliefs about tax compli- ance when individuals interact in a social network. It develops a model in which taxpayers possess a range of individual characteristics – including attitude to risk, potential for suc- cess in self-employment, and the weight attached to the social custom for honesty – and make an occupational choice based on these characteristics. Occupations differ in the pos- sibility for evading tax. The social network determines which taxpayers are linked, and information about auditing and compliance is transmitted at meetings between linked tax- payers. Using agent-based simulations, the analysis demonstrates how attitudes and beliefs endogenously emerge that differ across sub-groups of the population. Compliance behaviour is different across occupational groups, and this is reinforced by the develop- ment of group-specific attitudes and beliefs. Taxpayers self-select into occupations accord- ing to the degree of risk aversion, the subjective probability of audit is sustained above the objective probability, and the weight attached to the social custom differs across occupa- tions. These factors combine to lead to compliance levels that differ across occupations.

Ó2012 Elsevier B.V. All rights reserved.

1. Introduction

Tax evasion is the illegal concealment of a taxable activity. Measuring how much economic activity is concealed will al- ways be difficult since those who engage in evasion have every motivation to hide their activities. Even so, the estimates that are available from official sources (such asRevenue & Customs, 2010) and from academic researchers (Schneider & Enste, 2000) are in agreement that evasion is an economically significant activity. This emphasises the importance of understand- ing the decision process of a taxpayer when choosing whether to comply with tax law or to engage in evasion. A good theory of the compliance decision is essential for designing an audit policy that deters evasion.

The initial analysis of the compliance decision byAllingham and Sandmo (1972)models the taxpayer as facing a decision under risk, with the extent of evasion chosen to maximise expected utility. The model provides precise comparative statics predictions, but these are not always in accord with data (Clotfelter, 1983; Crane & Nourzad, 1986) or intuition. In particular, when evaluated using levels of the audit probability and the fine rate close to those observed in practice, the model predicts

http://dx.doi.org/10.1016/j.joep.2012.09.002 0167-4870/Ó2012 Elsevier B.V. All rights reserved.

⇑ Corresponding author at: Department of Economics, University of Exeter, Streatham Court, Rennes Drive, Exeter EX4 4PU, United Kingdom.

E-mail address:g.d.myles@ex.ac.uk(G.D. Myles).

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that all taxpayers should engage in evasion. This has motivated numerous extensions of the standard model – surveyed by Pyle (1991) and Sandmo (2005)– but these extensions do not address its fundamental limitations.

Two sets of issues have to be addressed in constructing an improved model. First, behavioural economics has demon- strated that individuals generally do not evaluate risky prospects using the objective probabilities of events. In practice, deci- sions are made using subjective probabilities that can differ significantly from the objective probabilities (Kahneman &

Tversky, 1979). Contributions drawing on these ideas are made by al-Nowaihi and Dhami (2007), Arcand and Graziosi (2005), and Snow and Warren (2005). Second, there is now compelling empirical (Spicer & Lundstedt, 1976) and experimen- tal (Baldry, 1986) evidence that the tax evasion decision is not simply an individualistic gamble. Instead, a wide range of social and psychological factors enter the compliance decision.Gordon (1989)analyses a psychic cost of evasion,Myles and Naylor (1996)introduce a social custom into compliance, and the concept of tax morale (Torgler, 2002) subsumes a range of social and equity factors. For reasonable parameter values these recent models can predict the levels of evasion that are consistent with empirical data.

An issue that has not been given much attention is the processes through which attitudes towards compliance are formed. Attitudes and beliefs are not exogenous but must result from interaction with other taxpayers and with the tax authority. The appropriate method for modelling such interaction is a social network that allows endogenous evolution of attitudes and beliefs. Placing appropriate structure on the social network can also permit investigation of how the degree of separation determines the divergence of attitudes and beliefs that can emerge among distinctive social groups in a het- erogeneous society.

Attitudes and beliefs are not only important for how a taxpayer will act when confronted with an evasion opportunity:

they are equally important in determining whether a taxpayer has such an opportunity in the first place. This is because opportunities for evasion are very limited in most forms of employment. The deduction of income tax at source and third-party reporting make evasion of employment income very difficult, if not impossible. In contrast, income earned in self-employment (or entrepreneurship) is not taxed at source and can have limited third-party reporting. This makes it pos- sible to undertake evasion when in self-employment. When an individual makes a choice of occupation the possibility of evasion in self-employment must be taken into account, which makes occupational choice partly dependent on the per- ceived benefit of evasion.

This paper seeks to combine these ideas and to explore the endogenous emergence of group-specific attitudes and beliefs.

We embed a behavioural model of the evasion decision into a social network, through which information on the activities of the revenue service is transmitted. Individual taxpayers are heterogenous in several dimensions, such as skill in employ- ment, attitude to risk, and success in self-employment. We also include a choice between occupations that differ in the risk- iness of reward and the opportunity to engage in evasion. The model is analysed by simulation, which permits us to trace the tax evasion dynamics that emerge from repeated taxpayer interaction within the network. The endogenous separation of taxpayers into occupations with differing evasion opportunities creates different behavioural types who comply to different degrees and can develop differing attitudes and beliefs.

The central result that emerges from the analysis is that risk aversion, occupational choice, compliance, and attitude to evasion are inter-related and mutually reinforcing. The true probability of audit is unknown, so taxpayers form a subjective probability through information transmission via social interaction. The simulations show, first, that interaction can sustain a subjective probability of audit that exceeds the objective probability. Thus, the model provides an illustration of how be- liefs can be formed in subjective expected utility theory. Second, they demonstrate how taxpayers self-select into occupa- tions in a way that maximises the amount of tax evasion. Self-employment is risky, so it is chosen by those with lower degrees of risk aversion. But it also opens the opportunity to evade, and those with a low risk aversion will evade the most when given the opportunity. Hence, we see a process of self-selection of those who will evade the most into a situation where they can evade. The self-selection is reflected in the levels of compliance of the different occupational groups: com- pliance in the most risky occupation is lowest. The endogenous choice of occupation results in different groups having mark- edly different rates of compliance. The attitude toward compliance also differs across the occupational groups. The information exchange between people in the same occupation reinforces group beliefs, and sustains different social customs across groups. Taxpayers in the riskier occupation comply less, and this is mutually reinforcing with a lower value of the social custom. In this sense the network can permit group-specific social attitudes to develop.

The paper is structured as follows. Section2describes the separate components that are built into the model. Section3 provides analytical details on how these components are implemented. Section4describes the simulation results. Section5 concludes.

2. Modelling

This section describes the separate elements that constitute the model. The intention is to place them into the context of the literature.

2.1. Subjective beliefs

The analysis of the evasion decision byAllingham and Sandmo (1972)applied expected utility theory. The standard inter- pretation is that the expectation is taken using the objective probability of an audit. One criticism of the model is that it over-

predicts the extent of evasion when evaluated using the objective probability. This has motivated the application of different forms of non-expected utility theory to the evasion decision. These are surveyed inHashimzade, Myles, and Tran-Nam (2012).

The situation is referred to as one of risk when the decision maker knows the probabilities of events. However, these probabilities can be distorted into ‘‘decisions weights’’ to form the expected payoff. Rank dependent expected utility (Quiggin, 1981; Quiggin, 1982; Quiggin & Wakker, 1994) uses a particular weighting scheme to transform the objective probability of events into subjective probabilities and has been applied to the evasion decision byArcand and Graziosi (2005), Bernasconi (1998), and Eide (2001). Prospect theory (Kahneman & Tversky, 1979; Tversky & Kahneman, 1992) also uses a weighting scheme but payoffs are determined by gains and losses relative to a reference point. Applications to com- pliance includeal-Nowaihi and Dhami (2007), Bernasconi and Zanardi (2004), Rablen (2010), and Yaniv (1999).

Uncertainty occurs when the decision maker does not know the probabilities. It has been modelled by assuming the deci- sion maker forms a probability distribution over possible probabilities of outcomes. This gives rise to the concept of ‘‘ambi- guity’’ which has been surveyed inCamerer and Weber (1992)and applied bySnow and Warren (2005).

The non-expected utility model can predict the correct level of evasion for reasonable parameter values. This is because they permit the subjective probability of audit (the weighting on the payoff when audited) to be greater than the objective probability. They also open the possibility of designing compliance policy to manipulate the subjective nature of the decision (Elffers & Hessing, 1997). We incorporate these ideas into the analysis by assuming the probability of audit is subjective, and by providing an explicit process through which the subjective belief is formed. The model therefore provides an endogenous explanation of subjective probabilities that are systematically different from the objective probabilities.

2.2. Social customs

The experiments ofBaldry (1986)suggest that the evasion decision is systematically different from a straightforward gamble. One explanation for this finding is that choosing to evade results in costs being incurred. For instance,Bayer (2006)assumes that concealing income has a direct financial cost. A related interpretation is provided byLee (2001), who assumes a taxpayer can reduce the assessed income after audit by paying an additional cost (such as a reduction in return from using concealed investments or the cost of professional advice for securing income in non-taxable forms).

A different approach is to view these costs as psychic, rather than financial. Such psychic costs might arise through the fear of detection, or the shame of being exposed. Their magnitude may, therefore, reflect an individual’s underlying attitudes towards compliance – an important feature of psychological theories of tax evasion (e.g.,Kirchler, Hoelzl, & Wahl, 2008;

Weigel, Hessing, & Elffers, 1987).Gordon (1989)formally incorporates psychic costs into the evasion decision. He interprets such psychic costs as arising from the social setting in which the taxpayer operates, so are a result of the loss of social prestige or reputation. An alternative to the psychic cost is the ‘‘conscience parameter’’ ofEisenhauer (2006, 2008). In this formulation of the compliance decision an individual recognises that evading tax results in free-riding on the taxes paid by compliant taxpayers. This generates a sense of guilt for the tax evader. The guilt is represented by discounting the untaxed income by the moral equivalent of a tax rate.

An alternative interpretation of the psychic cost is that it represents the loss of the payoff from following a social norm of honest tax payment. Under this interpretation it becomes natural to assume that the additional cost is generated by explicit social interaction, with the cost an increasing function of the proportion of taxpayers who do not evade. This formulation cap- tures the idea that more social prestige will be lost the more out of step the taxpayer is with the remainder of society. This approach has been developed byDavis, Hecht, and Perkins (2003), Fortin, Lacroix, and Villeval (2007), Kim (2003), Myles and Naylor (1996), and Traxler (2010)to show that reputation effects can lead to multiple equilibria and epidemics of evasion.

The existence of additional costs seems essential to explain some features of the tax evasion decision. To capture under- lying attitudes towards compliance, we choose to include in the model a social custom of honest tax payment, so there is a utility gain from following the social custom. The social custom is influenced by interaction in the social network, which emphasises the importance of the links between individuals.

2.3. Occupational choice

There are two reasons why occupational choice is important in the context of evasion. Firstly, there are differences in the possibility of concealing income in different occupations. This is partly due to the operation of the tax system. For example, the UK employs the Pay-As-You-Earn system in which income tax is deducted directly from the salaries of employees. This prevents any opportunity for evasion (except in collaboration with the employer). Also, the nature of the occupation can ex- plain whether there is a tradition of payment in cash, and different occupations can support different social customs (Ashby, Webley, & Haslam, 2009). It is therefore important that the choice of occupation be built into the model. Occupational choice is not an issue that has featured prominently in the literature on tax evasion, althoughCowell (1981), Isachsen and Strøm (1980), and Trandel and Snow (1999)consider the choice between work in the regular and informal economy.

The choice of occupation also has another aspect that is of interest from a theoretical perspective. It is standard to assume that occupations differ in the combination of risk and reward that they offer. For instance, employment can be taken as the least risky occupation with all forms of self-employment having greater risk. Individuals allocate to occupations on the basis of their ability at that occupation and their attitude to risk. This is the basis of the analyses ofKanbur (1981) and Black and de

(1997), which address whether aggregate risk-taking is socially efficient. In particular, they are concerned with whether an inefficiently low proportion of individuals enter risky occupations and, if so, whether tax policy can be used to raise welfare.

Evasion has been incorporated into this model of occupational choice byPestieau and Possen (1991). The possibility of evasion in the risky occupation has an interesting implication: if there is too little risk-taking without tax evasion then the possibility of evading encourages risk-taking. In this case, setting policy to reduce evasion will drive risk-taking further from the social optimum. At the same time, a more relaxed tax enforcement would serve as an indirect subsidy and may, therefore, improve welfare. The converse of this argument is that taxation has a variance-reducing effect on earnings from self-employment (government engages in risk-sharing), and, therefore, encourages self-employment. Evasion has the oppo- site effect and raises the variance again. So, from this argument, policy should try to reduce evasion.

2.4. Social network

Tax evasion is an illegal act which has to be concealed from public view. Similarly, revenue services do not normally re- veal their audit strategies. Together, these imply that taxpayers are not fully informed and can gain from obtaining additional information. It seems natural to assume that information will not be publicly traded, but will be passed between taxpayers who are in a position of mutual trust. It is this situation that is modelled by the social network.

The importance of social contacts is supported by empirical evidence. There is a positive connection between the number of tax evaders known to a taxpayer and the level of that taxpayer’s own evasion (De Juan, Lasheras, & Mayo, 1994; Geeroms &

Wilmots, 1985; Spicer & Lundstedt, 1976; Wallschutzky, 1984; Webley, Robben, & Morris, 1988). This suggests that the com- pliance decision is not made in isolation by each taxpayer but is made with reference to the norms and observed behaviour of the general society of the taxpayer.

This social interaction is captured through the application of network theory, as described inGoyal (2009) and Jackson (2004). In particular, we wish to apply recent advances in the endogenous formation of networks (Page & Wooders, 2009) to track change in the network over time, especially changes produced by switches in occupational choice. There is some existing work using networks in evasion analysis.Korobow, Johnson, and Axtell (2007)considers agent-based simulations in a simple network.Franklin (2009)looks at more complex networks but with a simpler model of the compliance decision.

Networks have also been applied to the analysis of crime more generally (e.g.,Glaeser, Sacerdote, & Scheinkman, 1996).

The social network plays two roles. First, it transmits the social custom from one person to another. If two non-evaders meet then the importance of social custom of honest payment is increased for both, but if a non-evader meets an evader then it is reduced for the non-evader and increased for the evader. Second, the audit policy of the revenue service is not public information. Individuals infer its policy partly from their own experience and partly by receiving information about the experiences of others. The simulation approach we employ can be seen as an application of agent-based modelling (Bloomquist, 2004; Tesfatsion, 2006) with agent interaction controlled by network structure.

3. A model

In this section we model the formation of attitudes and beliefs as the outcome of social interaction, and opportunities as the outcome of occupational choice. This is achieved by applying the theory of network formation to track the links between taxpayers and the transmission of attitudes and beliefs, and combining this with agent-based modelling that incorporates a behavioural approach to describe individual choices.

There areNindividuals interacting repeatedly in each ofTdiscrete time periods. In every period individuals choose a pre- ferred occupation and an optimal level of evasion. Each individual is characterised by a vector of parameters

w;

q

;q¹;q²;z;p;

v

, where each parameter is independently distributed across taxpayers. The first five parameters are as- signed to the taxpayer at the outset of the analysis and remain constant. These parameters are:w, the wage in employment;

q

, the coefficient of relative risk aversion;qⁱ, the probability of success in self-employed occupationi,i= 1, 2; andz, the pay- off from following the social custom.

The remaining two parameters are updated through interaction in the social network. They are:p, the perceived (subjec- tive) probability of audit; andv, the weight attached to payoff from following the social custom.

We now describe how these variables enter into the choice problem of a taxpayer and how the subjective probability and weight attached to social custom are updated.

At the start of every period an individual has a choice between employment or entering one of two self-employment occupations. If employment is chosen the wage,w, is obtained with certainty. The self-employment opportunities are rep- resented as risky ‘‘projects’’. Projecti(i¼1;2) has a probability of success,qⁱ, a pay-off of

p

ⁱ_s, if successful, and a pay-off

p

ⁱ_uif unsuccessful, where

p

ⁱ_s>

p

ⁱ_u>0. Note that the probability of success is specific to an individual, whereas the payoffs are spe- cific to the projects and, therefore, are the same for all individuals undertaking a given project. That is, the mean and variance of the pay-off from projecti, conditional on the realisation ofqⁱfor individualh, are given by

E

p

ⁱjqⁱ_h

¼qⁱ_h

p

ⁱ_sþ1qⁱ_h

p

ⁱ_u; Var

p

ⁱjqⁱ_h

¼qⁱ_h1qⁱ_h

p

ⁱ_s

p

ⁱ_u

²

:

The unconditional mean pay-off of projectiis the expected value taken at the societal level:

E½

p

ⁱ ¼E E

p

ⁱjqⁱ_h

¼E qⁱ_h

p

ⁱ_sþ1qⁱ_h

p

ⁱ_u

¼

p

ⁱ_s

p

ⁱ_uE½qⁱ þ

p

ⁱ_u:

For example, ifqⁱis uniformly distributed between 0 and 1 across taxpayers, thenE½

p

ⁱ ¼

p

ⁱ_sþ

p

ⁱ_u=2. The unconditional var- iance (at the societal level) of projectiis

Varð

p

ⁱÞ ¼E Var

p

ⁱjqⁱ_h

þVar E

p

ⁱjqⁱ_h

¼

p

ⁱ_s

p

ⁱ_u²E½qⁱE½1qⁱ þ2

p

ⁱ_s

p

ⁱ_uVarðqⁱÞ

Project 1 is termed riskier than project 2 in the sense thatVarð

p

¹Þ>Varð

p

²ÞandE½

p

¹PE½

p

². A strict inequality appears to be a more interesting situation than a mean-preserving spread, because of the trade-off between the mean and the variance at the societal level. This can be obtained by imposing various conditions on the distribution of

p

ⁱandqⁱ.¹In particular, assuming

p

¹_u<

p

²_u;

p

¹_s>

p

²_s;

p

¹_s

p

¹_u¼

p

²_s

p

²_u, and identical distributions forqⁱ, results inVarð

p

¹Þ>Varð

p

²ÞandE½

p

¹>E½

p

². Such a parameterisation is employed further in the numerical simulations of the model. For individual agents, however, the expected pay-offs and the variances differ, according to their individual probabilities of success.

Both projects are riskier than employment, in the sense that for each agent the wage in employment is certain. In the simulations we also assume that, at the societal level, the mean gain from self-employment is larger than the mean gain from employment,E½

p

¹>E½

p

²>E½w. This assumption appears realistic, and it adds to the trade-off between the mean and the variance in the pay-offs across occupations at the societal level.

It is not possible to evade tax in employment: the possibility arises only when self-employment is chosen. Even so, every taxpayer has a belief,p, over the probability of audit. The value of the perceived probability of detection is updated through the experience of the taxpayer with audits and through exchange of information when meeting other taxpayers. The choice of occupation and the choice of evasion level involve risk. Each taxpayer has a (constant) degree of relative risk aversion measured by the risk aversion parameter,

q

. Taxpayers behave as if they maximise subjective expected utility and, for ana- lytical tractability, we assume throughout a CRRA form for utility:

UðYÞ ¼Y^1q1

1

q

^{: ð1Þ}

There is a social custom that rewards honest tax payment. The payoff from the social custom is given byzand the individual weight, or the importance, assigned to this payoff by the taxpayer is determined by

v

. Hence, compliance generates an addi- tional utility from the social custom of

v

z. At each point in time the payoff is a fixed parameter for each taxpayer, but the weight changes over time through interaction with other taxpayers in the network.

In employment there is no opportunity for evasion. The taxpayer obtains a payoff given by V0¼½ð1

s

Þw^1q1

1

q

^þ

v

z;

where

s

is the constant marginal tax rate. The possibility of tax evasion makes the choice of self-employment a compound lottery: the outcome of the project is random, as is the outcome of choosing to evade. If self-employment occupation iis chosen the outcome

p

ⁱ_sor

p

ⁱ_uis randomly realised, with probabilitiesqⁱand 1qⁱ, respectively. Those in self-employment occupationiare then audited, with a fixed probability. If evasion is discovered then unpaid tax is reclaimed and a fine is imposed on unpaid tax. We may therefore define the expected payoff from the optimal choice of evasion in self-employment occupationiin state

v

^{, (}

v

¼s;u) as

Vⁱ_v¼ max

Eⁱv2½0;pⁱ_v phð1

s

Þ

p

ⁱ_vf

s

Eⁱ_vi1q

1

1

q

^{þ ð1pÞ}

ð1

s

Þ

p

ⁱ_vþ

s

pE

v

ⁱ

h i1q

1 1

q

^þ

v

z1_Ei

v¼0

½ 8>

<

>:

9>

=

>;;

whereE

v

ⁱis the amount of evasion in state

v

for occupationi, andf>1 is the fine rate. The term1½Ais an indicator function that takes the value one ifAis true and zero otherwise: the payoff from the social custom is obtained if there is no evasion.

The expected payoff from the compound lottery describing occupationiis then

Vⁱ_e¼qⁱVⁱ_sþ ð1qⁱÞVⁱ_u: ð2Þ

The choice of occupation is made by comparing the utility levels from employment and from self-employment. Hence, the chosen occupation is given by the maximum ofnV0;V¹_e;V²_eo

.

A network is modelled as a set of bidirectional links. An example of a network is illustrated inFig. 1. In this example indi- vidual 1 is linked to individual 2; individual 2 is linked to individuals 1 and 3; individual 3 is linked to 2 and 4; individual 4 is linked to 3.

A network can be described by annnsymmetric matrix of zeros and ones. For example, the network shown inFig. 1is described by matrixA:

1 We are grateful to the anonymous referees for helping to clarify this point.

A¼

0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 2

66 64

3 77 75:

In matrixAthe first row, representing the links of individual 1, has a single 1 in column 2; the second row, representing the links of individual 2, has 1s in columns 1 and 3, etc. That is, the element in rowiand columnjof matrixAis defined as

Aij¼ 1 ifiandjare linked in the network;

0 otherwise:

In the simulation, the network is created at the outset and does not change.²The network determines who may meet whom to exchange information. In each period a random selection of meetings occur; this is described by a matrixCof zeros and ones which is randomly selected every period. Individualsiandjmeet during a period ifAijCij¼1. At a meeting ofiandjthere is a probability that information is exchanged. When information is exchanged it consists of three elements: the taxpayer’s subjec- tive probability of audit, whether or not the taxpayer was compliant in that period, and whether or not the agent was audited.

The probability of information exchange depends on the occupational groups to whichiandjbelong; the probability is highest when they are in like occupations. The probabilities of information exchange occurring at a meeting are given byp_ij where i;j¼e;1;2.

The choice of occupation in periodtþ1 is made on the basis of a subjective belief~ptþ1.We consider two different pro- cesses for the formation of~p_tþ1. As studies have reliably demonstrated important deviations from Bayesian inference (e.g.

Grether, 1980), we allow for non-Bayesian updating. The first process, which is qualitatively similar to a Bayesian process, is to assume that individuals feel marked as targets if they are audited, so that one audit is believed likely to be followed by another. We term this the ‘‘target effect’’. In contrast, those not audited in a period believe they are less likely to be audited in the next period. Formally, if audited in periodt, an individual’s belief about being audited in the next period is raised to the levelP, otherwise it decays. The updating rule for the subjective probability is therefore

p~tþ1¼Xⁱ_tPþ 1Xⁱ_t

dpt; d2 ð0;1Þ; P2 ½0;1; ð3Þ

whereXⁱ_t¼1 if agentiwas audited in periodtandXⁱ_t¼0 otherwise. Thus, the perceived probability of evasion of being de- tected is determined by the individual’s own past experience and by the past experience of a randomly met member of that individual’s social network. The process in(3)can also be written as

Fig. 1.Representation of network.

2Another possibility would be to have the network revised as a consequence of chosen actions, i.e. employed and self-employed belonging to different social networks.

~ptþ1¼ P2 ½0;1 if audited att;

dpt; d2 ½0;1 otherwise:

ð4Þ

The second process we consider captures the ‘‘bomb-crater effect’’ documented experimentally byGuala and Mittone (2005), Kastlunger, Kirchler, Mittone, and Pitters (2009), Maciejovsky, Kirchler, and Schwarzenberger (2007), and Mittone (2006). In this process, a taxpayer who has been audited in one period believes that they will not be audited in the next, but the belief slowly rises over time. The process is therefore described by

~ptþ1¼ 0 if audited att;

p_tþdð1p_tÞ; d2 ½0;1 otherwise:

ð5Þ

After occupational choice is made,if an information exchange occursat a meeting with another individual, the subjective probability (formed according to either process) is updated according to the common rule

pⁱ_tþ1¼

l

epⁱ_tþ1þ ð1

l

ÞX^j_tPþ 1X^j_t e p^j_tþ1

h i

;

l

2 ð0;1Þ; which can also be written as

pⁱ_tþ1¼

l

epⁱ_tþ1þ ð1

l

ÞP ifjaudited att;

l

epⁱ_tþ1þ ð1

l

Þep^j_tþ1 otherwise:

(

Note that under the target effectP¼ep^j_tþ1ifjwas audited att, and so the updating rule reduces topⁱ_tþ1¼

l

epⁱ_tþ1þ ð1

l

Þep^j_tþ1. Under the bomb-crater effect, however, although an agent that has just been audited believes that theirpersonalprobability of audit is zero,epⁱ_tþ1¼0, they do not believe that this probability applies to other taxpayers. Hence, the updating rule reflects the assumption that agenti’s perceived probability of audit may rise after information exchange with agentjifilearns thatj has just been audited, even thoughj’s own perceived probability drops to zero.³

The importance attributed to the social custom is also determined by interaction in the social network. Each individual is initially assigned a random level of importance,

v

ⁱ₀. This value is updated after each information exchange with another tax- payer. The updating process is described by

v

ⁱtþ1¼ 1

XðiÞ þ1

v

ⁱtXðiÞ þ1_E^j

t¼0

½

h i

; ð6Þ

whereXðiÞis the number of previous meetings foriat which information was exchanged. Hence,

v

ⁱ_tþ1>

v

ⁱ_tif information is exchanged with an honest taxpayer, and

v

ⁱtþ1<

v

ⁱtif information is exchanged with an evader.

4. Simulation

The network model described above is simulated to investigate the nature of the equilibrium and the consequences of alternative updating rules on beliefs. In this context, equilibrium is a state in which aggregate behaviour is stationary around a steady-state level. Even in equilibrium, however, some amount of variation always remains because of randomness in the outcome of self-employment and the selection of taxpayers for audit.

This section summarises and discusses the most significant findings that emerge from the simulations. Results are re- ported for the two methods of updating beliefs in Eqs.(4) and (5). In addition, for the target effect, we also consider the effect of varying the probability of exchanging information. The parameter values and the distributions for those random variables that remain constant across the simulations are given in the Appendix. As discussed previously, we set the parameter values such that, on average, the payoff from self-employment will exceed that from employment.⁴

4.1. Target effect

In the case of the target effect the subjective probability is increased after an audit and decays when no auditing occurs.

Two set of results are given for this process of belief formation, which differ in the probability of information exchange be- tween different groups. Both sets of results are based on a true audit probability of 0:05 and a rate of decay in belief of d¼0:75.

The first set of results emphasises the differences that can emerge between groups by assuming that, when two taxpayers in the same occupation meet, information is exchanged always, but when two taxpayers in different occupations meet no information is exchanged. This is termedfocussed information exchange.

The results are summarised inFig. 2. The simulation is run for 200 periods. It can be seen that the effect of the initial ran- dom assignment of values to the subjective probability and the honesty weight is negligible after about 20 periods. The

3 We are grateful to an anonymous referee for raising this point.

4 The value of the social custom,z, is measured in units of utility. Therefore, althoughzappears constrained to take very small values, these values are commensurate with the values taken by the utility function in Eq.(1). Thus, with given parameterisation, a true report increases the utility of an ‘‘average’’

individual by about 10%.

proportions of the population in employment, risky self-employment, and less risky self-employment are 30%, 20%, and 50%, respectively. The level of compliance – measured by the proportion of agents declaring true income – is lowest for occupa- tion 1 (about 24%), which is the riskier of the two forms of self-employment. Occupation 2 has a rate of compliance of about 53%, about twice that of occupation 1. The remaining three figures explain the source of this difference. What is interesting is that the difference in compliance between occupations does not come from the subjective probability. The average belief of taxpayers in both occupations is approximately 0.15. This is much higher than the true probability of 0.05, but does not ex- plain the different compliance rates. The employed learn about audits only from self-employed who have been audited and switched into employment as a result. Hence, the subjective probability of the employed decays, on average, to just below the true value. The second driver of the difference in compliance is the weight given to the social custom. This is significantly lower in occupation 1 than in occupation 2, and close to 1 among the employed. The social custom reinforces the separation by risk aversion, and these jointly determine the compliance outcome.

The network effects can be seen to endogenously generate a culture of non-compliance that varies across groups. The non-compliance is not driven by differences in beliefs but by self-selection into occupations according to risk aversion, and is reinforced by the emergence of distinct group-specific social customs. This illustrates the process of endogenous behavioural differences among population sub-groups.

The second set of results report the outcome withdiffused information transmission. In this case there is a positive prob- ability (0.15) that a meeting between taxpayers in dissimilar occupations results in information exchange. In addition, the probability of information exchange at meetings between members of the same occupation is reduced (compared to the results inFig. 2) to 0.75.Fig. 3shows the effect that this has upon the outcome of the simulation. Compared toFig. 2there is very little change in the rate of compliance (but it is slightly higher for self-employed occupation 1), the separation by risk aversion, or the levels of the subjective probability. The only significant difference between the two set of results is seen in the weight attached to the social custom. The diffused information transmission means that some employed tax- payers exchange information with evaders, and evaders in the self-employed occupations have an increased probability of meeting a compliant taxpayer. As a consequence, the social custom weight among the employed is reduced, while among occupation 1 it is increased. This enhanced importance of the social custom in occupation 1 explains the slightly higher compliance level of that group. The proportion of the population belonging to each occupational group remains approx- imately unchanged.

The central message of these results is that sub-groups of the population can endogenously form different attitudes to compliance. These differing attitudes combine with self-selection into occupations to produce significantly differing levels of compliance across occupations. The social network also results in the subjective probability of audit being above the true value for the self-employed. The self-employed groups hold similar beliefs, which are distinctly different from those of the employed. These features highlight the importance of social networking effects in explaining patterns of compliance.

1

Compliance

7

Risk aversion 1

SE1 7 0 8

SE1

SE2 6

0.8 SE2

Total 6

0.6 5

Emp

0.4 4 SE1

SE2

0 2 3

SE2

0.2 3

0 50 100 150 200

0 20 50 100 150 200

Subjective beliefs

0 50 100 150 200 0 50 100 150 200

Honesty weight

0.5 1

Honesty weight

0 4

Emp

SE1 0 8

0.4 SE1

SE2 0.8

0.3

SE2 Total _0.6 0.3

0.2 0.4

0 1 0 2

0.1 0.2

Emp SE1 SE2 Total

0 0

Emp SE1 SE2 Total

0 50 100 150 200

0 00 50 100 150 200

Fig. 2.Focussed information exchangeðpee¼1;pe1¼0;pe2¼0;p11¼1;p22¼1;p12¼0Þ.

4.2. Bomb-crater effect

The final set of results explore the outcome when the probability of audit is updated according to the bomb-crater pro- cess. In this case subjective probability is revised down after an audit, but then tends upward until the next audit occurs. The

7

Risk aversion 1

Compliance 1 7

SE1

0.8 SE2 6

Total 0.6 5

4

Emp

0 4 4 SE1SE1

SE2 0.4

3

SE2 0.2

0 50 100 150 200

0 50 100 150 200 2

0

Subjective beliefs

0 50 100 150 200

0 50 100 150 200

Honesty weight 0.5

E

1 0 4

Emp

SE1 0 8

0.4 SE1

SE2 0.8 0.3

SE2 Total 0.6

0.2 0.4 Emp

0 1 0 2

SE1

0.1 0.2 SE2

Total

0 0

Total

0 50 100 150 200

0 00 50 100 150 200

Fig. 3.Diffused information exchangeðpee¼0:75;pe1¼0:15;pe2¼0:15;p11¼0:75;p22¼0:75;p12¼0:75Þ.

1

Compliance

7 Risk aversion

1 7

6 0.9

0.9

5 4

Emp SE1

0.8 4 SE1

SE2

SE1 SE2 T l ³

SE2

SE1 SE2 Total ³

0.7 2

0 50 100 150 200

Honesty weight

0 50 100 150 200

1 1

Subjective beliefs

0.9 0 9 0.9 0.9

0.8 0.8

.8 0.7 Emp

0.7

Emp 0 6 SE1

0 6 0.6 SE2

0.6 Total

0.5

E SE1 SE2 T t l

0.4 0.5

Emp SE1 SE2 Total

0 50 100 150 200

0 50 100 150 200 0.5

0.4

Fig. 4.Bomb crater process for subjective probabilityðpee¼0:75;pe1¼0:15;pe2¼0:15;p11¼0:75;p22¼0:75;p12¼0:75Þ.

results reported inFig. 4are for diffused information transmission. The true audit probability is again chosen to be 0.05 and the rate of increase in belief isd¼0:05.

The bomb-crater effect leads to a much higher level of compliance across occupations than the target effect. For the same values of the parameters in the simulations, about 86% of taxpayers in the risky occupation and about 92% in the less risky occupation report their true income. This high rate of compliance is a consequence of the infrequent audits. The infrequency of audits means that there are numerous periods in which a taxpayer is not audited and in each of these periods the sub- jective probability increases. This effect is especially marked for a taxpayer who always chooses to be employed: no audit is ever undertaken so the subjective belief increases toward unity. This may seem inconsistent, but, owing to the impossi- bility of non-compliance in employment, an interpretation of the effect is that employed taxpayers behave ‘‘as if’’pis unity.⁵ The occupational groups are still characterised by differing degrees of risk aversion, but for this simulation there is little to separate the employed and those in the less risky self-employment occupation. Due to the high rate of compliance, there is an increased weight attached to the social custom for honesty. The major distinction between the bomb-crater effect and the target effect is that these weights become more similar across occupations, although the pattern is the same as under the target effect: for the individuals in risky occupation the weight, on average, is the lowest, and for the individuals in employ- ment the weight, on average, is the highest, but the differences between groups are small. The proportions of population in employment, risky self-employment and less risky self-employment are 36.1%, 18.6%, and 45.3%, respectively. Comparison with the target effect scenario shows that under the bomb-crater effect more agents choose employment (the size of this group is larger by 20%), and fewer agents choose self-employment (the size of the group in the risky occupation is lower by 7%, and in the less risky occupation it is lower by 9.4%). This is consistent with the overall higher compliance rates across groups and higher subjective probability of audit, which makes self-employment less attractive from the viewpoint of the opportunity to evade tax.

4.3. Summary statistics

A summary of the descriptive statistics for the variables inFigs. 2–4is given inTable 1. The means and the standard devi- ations are calculated over the last 50 simulated periods.Table 2shows the averages over occupational groups for the wage in

5We are grateful to an anonymous referee for this interpretation.

Table 1

Means and standard deviations (in parentheses) by occupational group.

Target effect Bomb-crater effect

Focussed exchange Diffused exchange Diffused exchange

SE1 SE2 EM SE1 SE2 EM SE1 SE2 EM

Risk 2.665 5.325 6.092 2.913 5.195 6.205 2.940 5.438 5.529

aversion (.034) (.016) (.050) (.027) (.020) (.053) (.009) (.001) (.000)

Honesty .293 .722 .966 .506 .689 .818 .939 .940 .972

weight (.006) (.001) (.004) (.003) (.001) (.002) (.000) (.000) (.000)

Compliance .240 .533 1 .322 .532 1 .864 .920 1

(.026) (.014) – (.020) (.015) – (.026) (.012) –

Beliefs .150 .155 .030 .158 .155 .038 .616 .612 .940

(.022) (.010) (.004) (.015) (.010) (.006) (.015) (.015) (.002)

Table 2

Success probabilities and pay-offs by groups.

Target effect Bomb-crater effect

Pr success Exp pay-off StDev Pr success Exp pay-off StDev

SE1

Project 1 0.819 14.192 3.849 0.824 14.247 3.802

Project 2 0.400 9.602 1.960 0.437 9.746 1.984

Employment 6.748 6.049

SE2

Project 1 0.410 10.106 4.920 0.416 10.159 4.929

Project 2 0.575 10.298 1.978 0.578 10.311 1.976

Employment 5.148 4.751

EM

Project 1 0.473 10.728 4.993 0.473 10.729 4.993

Project 2 0.472 9.886 1.997 0.467 9.869 1.996

Employment 13.046 12.586

employment and probabilities of success in self-employment, as well as the mean and the standard deviation of the pay-offs in self-employment.

One can clearly see the outcome of the self-selection process, in particular, for the distribution of earnings. For individuals who choose employment the probability of success in either self-employment occupation is below average, whereas their wage in employment is significantly above average. At the same time, for individuals in self-employed occupation 1 the probability of success in occupation 1 is above average, and the probability of success in occupation 2 is below average;

the converse holds for individuals in self-employed occupation 2. The wage in employment is below the average pay-off to both self-employment occupations. Individuals who self-select in occupation 1 earn, on average, a higher payoff but with a higher variance than they would in occupation 2. At the same time, individuals who self-select in occupation 2 earn, on average, a higher payoff with a lower variance than they would in occupation 1. This is consistent with self-selection of indi- viduals with lower risk aversion into occupation 1.

5. Conclusion

An understanding of the individual tax compliance decision is important for revenue services. Their aim is to design pol- icy instruments to reduce the tax gap (the difference between anticipated and actual tax revenue). Empirical evidence dem- onstrates that a wide range of factors, including social groupings and network effects, may impact upon the individual compliance decision.

The research we report in this paper combines ideas from behavioural economics and social networks to model occupa- tional choice and tax compliance in an integrated framework. The analysis is based on the consequence of taxpayers possess- ing social connections through which information and attitudes relevant to the compliance decision are transmitted. The model accommodates differences in preferences, in productivity, and in opportunities for evasion. Occupational choice oper- ates as a form of self-selection that places those who will evade into situations where evasion is possible. Social interaction results in the subjective probability of audit differing from the objective probability. Combined with a social custom that rewards compliance, this can generate relatively high levels of compliance (when compared to the ‘‘standard’’ model).

The simulations have considered two different processes for the formation of subjective beliefs. These are distinguished by whether an audit causes an increase in the subjective probability (the target effect) or a reduction (the bomb-crater ef- fect). Although these processes are very different, the important qualitative properties of the simulations are the same in both cases. First, taxpayers self-select into occupations according to the degree of risk aversion. Second, the subjective prob- ability of audit can be sustained above the objective probability. Third, the weight attached to the social custom differs across occupations, a finding relevant to the literature on the evolution of social norms (Bendor, 2001; Boyd & Richerson, 1994).

Finally, these factors combine to lead to a compliance level that is lower in the riskier occupation.

The model has also demonstrated how it is possible for attitudes and beliefs to emerge endogenously that differ across sub-groups of the population. The population is heterogenous in characteristics and chooses occupational groups on the ba- sis of characteristics. The behaviour is different across occupational groups, and this is reinforced by the development of group-specific attitudes and beliefs.

A prominent avenue for future work is to relax the assumption of random auditing. In practice, only a small proportion of audits are selected in this manner, with the remainder targeted according to risk-based rules. This extension would allow for an analysis of the effectiveness of alternative strategies for targeting audits when taxpayers form beliefs about auditing from interaction in a social network. It would also be possible, followingRablen (in press), to incorporate the cost of audit and imperfect audit effectiveness into the model. In this paper we assumed that an audit always detects the full amount of eva- sion, i.e. is perfectly effective. This would enable an analysis of the trade-off in audit strategy between audit probability and effectiveness, in particular, the effects of introducing so-called ‘‘light-touch’’ audits, which cost a fraction of a traditional tax audit, but which may also be less effective.

Acknowledgments

This project was financed by the HMRC/HMT/ESRC Joint Research Programme ‘‘Tax Policy and Operation in the Context of Economic and Societal Change’’ (Grant ref: RES-194-23-0002). Their support is gratefully acknowledged. The views ex- pressed in this paper are those of the authors and cannot be attributed to H.M. Revenue and Customs, H.M. Treasury or H.M. Government.

Appendix A

Parameter values Tax rate:

s

¼0:25 Fine rate:f¼1:5

Payoffs in occupation 1:

p

¹s ¼16;

p

¹u¼6 Payoffs in occupation 2:

p

²_s ¼12;

p

²_u¼8 Weight in information exchange:

l

¼0:75 Belief following an audit:P¼1

Number of periods:T¼200 Number of taxpayers:N¼1000 Probability distributions

Wage in employment:wU½0;16 Risk aversion:

q

U½0;10

Success in occupationi:qⁱU½0;1

Initial belief on audit probability:p₀U½0;1

Importance assigned initially to social custom:

v

0U½0;1 Value of social custom:zU½0;310⁵

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